Dynamic contributions to the optical Stark effect in semiconductors

We present femtosecond time-resolved optical pump-probe measurements of the coherent excitonic nonlinear optical response in GaAs quantum wells. The data exhibit features that cannot be explained by the conventional description of the optical Stark effect as a rigid blueshift of the exciton absorption spectrum when the pump field is present. Using the semiconductor Bloch equations we develop a model that permits the pump-induced changes in the probe transmission to be calculated for arbitary laser pulse profiles, both chirped and unchirped. The results demonstrate that the amplitude and phase spectral structure of the probe strongly influence the detection signal when the pulses are ultrafast (i.e., faster than the polarization decay time), in marked contrast to the normal assumptions made in transient optical spectroscopy. We examine these dynamic contributions in terms of four-wave mixing of different frequencies in the probe spectrum, and show that in adition to the optical Stark shift normally measured, there is an additional component arising from dynamic changes in the refractive index due to resonantly enhanced cross-phase modulation.